The impact of Pb on the environment and human health and recent restrictions on its use in electronic devices are generating demand for Pb-free piezoelectric materials. Examples are now available commercially, but the full elastic-piezoelectric-dielectric (EPD) matrices needed for device design, including over a range of operating conditions, have not yet been published. The standard IEEE EPD matrix measurement method needs four sample geometries, making it inconvenient and increasing errors. Here, we present an alternative method combining resonant ultrasound spectroscopy with optimization algorithms to measure the EPD matrix from a single exact cube sample. The Levenberg–Marquardt (LM) and Nelder–Mead (NM) optimizations are compared in refining the independent parameters. Both give convergent solutions, but the LM algorithm is more accurate and efficient. The single-sample approach was used to obtain results from Pb-free Na _1/2 Bi _1/2 TiO ₃ (PIC 700, PI Ceramics, Lederhose, Germany) piezoceramic ( $\infty $ mm sample symmetry) characterized with the standard IEEE method at ambient temperature and with the single-sample method at ambient temperature and additionally up to 80 °C. The results are validated with the laser Doppler vibrometry via mode shape reconstruction and comparison with finite-element analysis (FEA). They demonstrate that convenient measurement of the EPD matrix of Pb-free materials with temperature dependence is possible, providing a crucial capability for the adoption of these materials in devices.

中文翻译：

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适用于传感器设计人员的无铅PIC 700的全套材料特性

铅对环境和人类健康的影响以及最近在电子设备中对其使用的限制，都产生了对无铅压电材料的需求。实例现已可商购，但尚未公开器件设计所需的完整弹性-压电-电介质（EPD）矩阵，包括在一定范围的工作条件下。标准的IEEE EPD矩阵测量方法需要四个样本几何形状，这带来了不便并且增加了误差。在这里，我们提出了一种将共振超声光谱与优化算法相结合的替代方法，以从单个精确的立方样品中测量EPD矩阵。在细化独立参数时，对Levenberg-Marquardt（LM）和Nelder-Mead（NM）优化进行了比较。两者都提供收敛的解决方案，但是LM算法更准确，更高效。单样本方法用于获得无铅Na的结果 _1/2 Bi _1/2 TiO ₃（PIC 700，PI Ceramics，Lederhose，德国）压电陶瓷（ $ \ infty $ 毫米样品对称性），其特征在于在环境温度下采用标准IEEE方法，在环境温度以及最高80°C时采用单样本方法。激光多普勒振动法通过模式形状重建并与有限元分析（FEA）进行比较，验证了结果。他们证明，可以方便地测量与温度相关的无铅材料的EPD基质，为在设备中采用这些材料提供了至关重要的能力。